Question

The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown.

What is the greatest possible whole-number value of the congruent side lengths?

A.9 cm
B.10 cm
C.14 cm
D.15 cm

Answer 1

B.10 cm hopes this helps

Answer 2

C. 14 cm

Explanation:

According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the measure of the third side.

Given,

The longest side of an isosceles obtuse triangle measures 20 centimeters.

Let x be the measure of the other two congruent sides,

By the above property,

20 < x + x

20 < 2x

10 < x

Thus, the measure of congruent sides must be greater than 10 cm,

Now, In an isosceles obtuse triangle, the square of the longest side is greater than the sum of squares of the other two congruent sides.

`(20)^2>x^2+x^2`

`400>2x^2`

`200>x^2`

`10√(2)>x`

Since, √2 = 1.41421356≈ 1.41

`\implies x < 10* 1.41\implies x < 14.1`

Hence, the greatest possible whole-number value of the congruent side lengths is 14.

Option C is correct.